Why seven is common and two is rare
Two six-sided dice have 36 ordered outcomes. Seven can be made six ways: 1+6, 2+5, 3+4, 4+3, 5+2 and 6+1. Two can only be made by 1+1.
With independent dice, every roll uses the same probabilities. A long run without an eight does not make the next independent roll more likely to be eight. The table below also describes the first draw from a fresh Archipelago balanced cycle.
Archipelago draws 24 of the 36 outcomes
New standard games use balanced dice. Start with one of each ordered pair, draw without replacement for 24 rolls, then discard the remaining 12 and reset to all 36. An outcome already drawn cannot be selected again until the reset, but another pair with the same total can still appear.
This changes next-roll odds without guaranteeing a perfect histogram or banning repeated totals. Older games can retain independent dice, so check the game’s dice rule rather than assuming every recording uses the new system.
A worked next-roll example
A fresh cycle has five outcomes totalling six. If the first roll is a six, four of those outcomes remain among 35 pairs: the next-roll chance of six is 4/35, about 11.43%. If the first roll is another total, all five remain: 5/35, about 14.29%.
After the 24th draw, the next roll resets to 5/36, about 13.89%. The game’s live dice chart separates the long-run reference from conditional next-roll odds. Use that public chart; no guide can reveal a future roll.
Use probability to compare plans
Higher-probability tiles are valuable because they tend to produce more over time. Resource diversity and useful combinations still matter: plenty of wool does not automatically pay for a city.
Spread your economy across useful resources and numbers, and keep trading options open. Balanced dice reduce some variation; they do not guarantee that a specific player receives the cards they need.
| Total | Ways out of 36 | Probability |
|---|---|---|
| 2 | 1 | 2.78% |
| 3 | 2 | 5.56% |
| 4 | 3 | 8.33% |
| 5 | 4 | 11.11% |
| 6 | 5 | 13.89% |
| 7 | 6 | 16.67% |
| 8 | 5 | 13.89% |
| 9 | 4 | 11.11% |
| 10 | 3 | 8.33% |
| 11 | 2 | 5.56% |
| 12 | 1 | 2.78% |